Optimization of Cold Chain Logistics with Fuzzy MCDM Model

Abstract

Vaccines are biological products containing a weakened, inactivated part of bacteria or viruses that are not harmful to the human body. Vaccine manufacturers and distributors should always store vaccines at the right temperature. To do this task, manufacturers and distributors need to manage cold supply chains to the required standards. Cold chain management helps manufacturers control and keep vaccines at the right temperature while ensuring quality and extending their expiration date. That will help businesses in the medical industry reduce economic losses, avoid waste, and bring more significant benefits to patients. The selection and evaluation process for logistics suppliers, especially those who deal with low-temperature storage, considers many factors to reduce the potential waste of products from poor storage strategies. The author introduces an integrated approach to solve such a fuzzy multiple criteria decision-making (MCDM) problem based on the Fuzzy Analytical Hierarchy Process (FAHP) model and an Interactive and Multi-criteria Decision-Making in Portuguese Model (TODIM) model methods under the fuzzy linguistic environment. In this work, the SF-AHP method derives criteria weights in the first stage, and then a TODIM method is presented to identify the ranking of logistics providers. Finally, the authors present a case study on the evaluation and selection of cold chain logistics suppliers to demonstrate the applicability of the proposed fuzzy MCDM model.

1. Introduction

Cancer is the second leading cause of death after cardiovascular disease from general sickness. Therefore, cancer prevention and treatment are a major concern not only of the health sector, but also of the social community. In addition to the three classic methods of surgery, chemotherapy, and radiation therapy, immunotherapy is the fourth method being researched and developed. In this immunotherapy, vaccines are the most proactive, early, specific, and promising direction [1,2].

Vaccines need to be stored and transported according to certain standards to ensure vaccine quality is maintained. Storage and transportation of vaccines play an important role in increasing a vaccine’s effective disease prevention rate. Vaccines that are not stored and transported properly can lead to problems such as reduced potency, reduced effectiveness of vaccines, huge costs from wasted unmaintained vaccines, and losing the trust of vaccine recipients.

The methods of storage for vaccines are specially done due to the importance of the product with hopes to reduce waste [3,4]. In order to maintain vaccine quality, the drug cold chain system is utilized in order to securely transport from production to consumption [5]. This logistics method is different compared to generic cold chain transportation method such as the utilization of different batch sizes, operation costs, and coordination between the parties involved. It is also highly unpredictable and requires strict quality checks between each part of the chain [6]. Following successful testing and clearance for vaccine manufacture, each vaccine dosage must be transmitted throughout the world to hospitals, clinics, vaccination programs, or medical facilities. The vaccine must be safely preserved until it is delivered to the individual that requires vaccination.

In order to ensure the quality of low-temperature-maintained products such as beverages, food, and pharmaceuticals, the cold supply chain is used in order to maintain such temperature throughout the delivering and transportation process. The cold vaccine chain, which comprises a refrigerator, freezer, cold box, cold chamber, and carrier, is used to properly preserve vaccines and maintain vaccine quality. This worldwide network can keep vaccines at the proper temperature throughout the whole process, from the production line to when the vaccine is injected into the syringe [7].

Decision-making problems are becoming increasingly complex to solve due to the numerous aspects to consider, particularly in today’s sectors owing to the rapid growth of information technology, which has resulted in an expanding number of options. Because of the increasing complexity of decision making, many options and comparisons force managers and professionals to be cautious in their decisions. Hence, they require assistance from a Decision Support System (DSS) combined with MCDM techniques to solve decision-making problems with multiple criteria and options [8]. The most well-known MCDM methods are Analytical Hierarchy Process (AHP) [9], The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [10], ÉLimination et Choix Traduisant la REalité (ELECTRE) [11]. Many studies have revealed that traditional MCDM approaches cannot solve problems in a dynamic environment. As a result, when paired with fuzzy set theory and application, it is feasible to solve decision makers’ uncertainty [12]. A lot of research employs Pythagorean fuzzy sets, intuitive fuzzy sets, and neutral sets to gather information and expert opinions more accurately and unambiguously. This add-on includes a membership function with three dimensions to provide more exact information [13].

Multiple Criteria Decision Making (MCDM) is emerging as a discipline in operations research. While fuzzy theory was included into MCDM research, the approaches were essentially developed along the same lines. This has made the fuzzy MCDM model become an effective tool to assist decision makers in choosing the optimal solution. Using FMCDM methodology is one of the strategies that can improve decision-making accuracy. This is a frequently used strategy that combines fuzzy techniques to solve uncertainty from the decision maker. The fuzzy MCDM model has been applied in many different fields such as renewable energy [14], the food processing industry [15], Open Banking Business [16]. Only a few studies have considered the supplier selection problem for vaccine cold chain logistics. This is a reason why the authors introduced an integrated approach based on the combination of the Fuzzy Analytical Hierarchy Process (SF-AHP) model and an Interactive and Multi-criteria Decision-Making in Portuguese Model (TODIM) methods for cold chain logistics service provider selection under the fuzzy linguistic environment. In this work, the SF-AHP method derives criteria weights in the first stage, and then a TODIM method is presented to identify the ranking of logistics providers. The primary goal of this study is to propose a fuzzy MCDM model for cold chain logistics services provider evaluation and selection. The proposed approach is the first vaccine cold chain logistics provider evaluation and selection model in Vietnam using expert interviews and literature reviews. This is also the first study to provide a case study on evaluating logistics supplier in vaccine cold logistics that utilizes a combination of FAHP and TODIM models.

In the following sections of this paper, the authors discuss the criteria of cold chain logistics service providers, describe the research methodology, present a practical case study, and discuss results and recommendations for future research.

2. Literature Review

When using a fuzzy expert system (FES) in the MCDM approach, this FEss system employs fuzzy logic to handle qualitative and quantitative information and characteristics to assist decision-making experts by modeling and simulating their expertise [17]. There have been various studies about the application of MCDM models to solve complicated decision-making problems which involve multiple criteria. These models are applied in various fields and sectors. In the field of supply chain management, MCDM models are regularly applied to support solving problems such as facility location selection [18,19,20,21,22], supplier performance evaluation [23,24,25,26,27], distribution channel development [28,29], etc. Among these, supplier evaluation and selection processes, which involve multiple qualitative and quantitative criteria, are frequently supported by MCDM models.

Karsak and Dursun [30] developed an integrated fuzzy MCDM model to support the supplier evaluation and selection process of hospitals. The model employed Quality Function Development (QFD) methodology in combination with fuzzy information fusion and 2-tuple linguistic representation. The evaluation criteria are established based on the QFD method, and the criteria weights and performance scores of potential suppliers are calculated using House of Quality (HOQ) matrices. The proposed model was applied to a real-world case study of a hospital in Istanbul. Mao et al. [31] introduced a heterogeneous MCDM framework to support the sustainable supplier selection process. The proposed model was based on interval-valued intuitionistic fuzzy (IVIFNs) numbers and interactive multi-criteria decision making (TODIM) method. The proposed approach was applied to a real-world case study of a polymer manufacturer, and the result of the model was compared with the Simple weighted average method and fuzzy TOPSIS. Wang et al. [32] introduced a fuzzy MCDM model to support the supplier selection process of edible oil manufacturers. In this research, the selection criteria were taken from the Supply Chain Operation Reference (SCOR) model, while the analytic hierarchy process (AHP) was used to calculate the criteria weights, and the Data Envelopment Analysis (DEA) method was used to determine the performance score and ranking of the potential suppliers. The proposed model was applied to a real-world case study of an edible oil manufacturer in Vietnam. Mohammed et al. [33] introduced a hybrid MCDM-FMOO model to support the supplier selection and order allocation process. In this study, the authors utilized fuzzy AHP and fuzzy TOPSIS methods to assess and rank potential suppliers. Then, a Fuzzy Multi-Objective Optimization (FMOO) model was formulated to calculate the optimal order allocation plan. Nallusamy et al. [34] discussed the use of AHP in combination with fuzzy logic and Artificial Neural Network (ANN) in solving a supplier selection model. Badi and Pamucar [35] developed a hybrid Grey theory MARCOS model to support the supplier selection process of the iron and steel manufacturing industry. The proposed model was applied to a real-world case study of a Libyan iron and steel manufacturer. A comparative study was performed where the result of the proposed model was compared to that of three other MCDM methods: CODAS, TOPSIS, and VIKOR.

In recent years, sustainability has been a major concern to supply chains around the world. Therefore, there has been much literature about the application of MCDM models in the sustainable supplier selection processes of supply chains. Wang Chen et al. [36] developed a fuzzy MCDM approach to green supplier selection problems. The model utilized fuzzy AHP and fuzzy TOPSIS techniques to determine the ranking of potential suppliers while considering economic and environmental criteria. The proposed model was then applied to a real-world case study of a luminance enhancement film manufacturer. Quan et al. [37] introduced an MCDM-based approach to the green supplier selection process within a large group of decision makers setting. In this research, the authors utilized interval-valued intuitionistic uncertain linguistic sets to asset the performance of the potential suppliers regrading each evaluation criterion and an Ant colony algorithm was utilized to divide the large group of decision makers into subgroups. Then, a linear programming model was developed to calculate the weights of the criteria, and an extended MULTIMOORA model was used to rank the potential suppliers. Liou et al. [38] developed a combined approach to green supplier selection problems based on MCDM and data-mining techniques. The authors utilized a support vector machine (SVM) to identify important selection criteria from historical data, then, a fuzzy best worst method (BWM) was used to calculate the criteria weights, and finally, fuzzy TOPSIS was applied to rank the potential suppliers. Memari et al. [39] develop an MCDM-based decision support tool for the sustainable supplier selection process. The authors employ an intuitionistic fuzzy TOPSIS to evaluate potential suppliers across nine criteria. The proposed model was then validated through a real-world case study of an automotive spare parts manufacturer. Zhao and Guo [40] introduced a fuzzy entropy-TOPSIS model to evaluate the performance of potential green suppliers in the electric power industry. An empirical case study of a thermal power equipment supplier selection in China was performed to demonstrate the effectiveness and feasibility of the proposed model. Mohammed et al. [41] introduced a hybrid MCDM model to support a supplier selection process with a focus on resilient sourcing. The proposed model was built upon a combination of the DEMATEL method and MABAC-OCRA-TOPSIS-VIKOR (MOTV) methods. Additionally, Spearman rank correlation coefficient (SRCC) was also applied to examine the correlation between the suppliers’ ranking. The proposed approach was applied to a scrap metal supplier selection process of a steel manufacturer. The result suggested that the most important criterion was “trust”, followed by “cost”, while the least important one was “geographical location”.

3. Methodology

Multiple Criteria Decision Making (MCDM) is emerging as a discipline in operations research. While fuzzy theory was included into MCDM research, the approaches were essentially developed along the same lines. This has made the fuzzy MCDM model become an effective tool to assist decision makers in choosing the optimal solution. In this study, the author proposed a fuzzy MCDM model for assessing and selecting a cold chain logistics service provider in Vietnam. This study’s recommended approach consists of three key steps, and a research graph is shown in Figure 1.

Step 1. Determining the criteria affecting the evaluation and selection of logistics service provider process.

Step 2. Identifying the weight of criteria by a Fuzzy Analytic Hierarchy Process (FAHP) model.

Step 3: In the last stage, the TODIM approach is used to evaluate all potential cold chain logistics service providers on the criteria.

3.1. Theoretical Fuzziness

TFN is defined as (t,f,k), where t,f, and k (t ≤ f ≤ k) are parameters that determine the least likely value, most promising value, and highest conceivable value in TFN. TFN are depicted in Figure 2 and can be classified as follows [42]:

$$\left(\frac{x}{\tilde{M}}\right)=\{\begin{array}{cc}0,& \mathrm{if} x<f,\\ \frac{x-t}{f-t}& \mathrm{if} t\le x\le f,\\ \frac{k-x}{k-f}& \mathrm{if} f\le x\le k,\\ 0,& \mathrm{if} x>k,\end{array}$$

(1)

The following is an example of a fuzzy number.

$$\tilde{M}=(M^{o\left(y\right)},M^{i\left(y\right)})=\left[t+\left(f-t\right)y, k+\left(f-k\right)y\right],y \in \left[0,1\right]$$

(2)

$o\left(y\right)$ and $i\left(y\right)$ represent the left and right sides of a fuzzy number, respectively. Two positive TFN $\left(t_1,f_1,k_1\right)$ are used in the basic computations presented below $\left(t_2,f_2,k_2\right)$.

$$\begin{gathered} \left(t_1,f_1,k_1\right)+\left(t_2,f_2,k_2\right)=\left(t_1+t_2,f_1+f_2,k_1+k_2\right) \\ \left(t_1,f_1,k_1\right)-\left(t_2,f_2,k_2\right)=\left(t_1-t_2,f_1-f_2,k_1-k_2\right) \\ \left(t_1,f_1,k_1\right)\times \left(t_2,f_2,k_2\right)=\left(t_1\times t_2,f_1\times f_2,k_1\times k_2\right) \\ \frac{\left(t_1,f_1,k_1\right)}{\left(t_2,f_2,k_2\right)}=\left(t_1/t_2,f_1/f_2,k_1/k_2\right) \end{gathered}$$

(3)

3.2. Fuzzy AHP Model

The Fuzzy Analytical Hierarchy Process (FAHP) is a fuzzy variant of the Analytical Hierarchy Process (AHP) that addresses the limitations of AHP in working with uncertain decision-making situations. Let $X=\left\{x_1,x_2,\dots ,x_n\right\}$ be the set of objects and K$K=\left\{k_1,k_2,\dots ,k_n\right\}$ be the set of goals. Each item is taken, and an extent analysis of its aims is performed using Chang’s extent analysis approach [42]. As a result, each object’s extent analysis values can be acquired. These numbers are written as follows:

$$L_{k_i}^1,L_{k_i}^2,\dots ,L_{k_i}^m, i=1,2,\dots ,n$$

(4)

where $L_k^j\left(j=1,2,\dots ,m\right)$ are the TFNs.

The $i^{th}$ object’s fuzzy synthetic extent value is defined as:

$$S_i={\displaystyle \sum }_{j=1}^m{L}_{k_i}^j\otimes {\left[{\displaystyle \sum }_{i=1}^n{\displaystyle \sum }_{j=1}^m{L}_{k_i}^j\right]}^{-1}$$

(5)

The possibility that $L_1\ge L_2$ is defined as:

$$V\left(L_1\ge L_2\right)=su{p}_{y\ge x}\left[min\left({\mu }_{L_1}\left(x\right),\right),\left({\mu }_{L_2}\left(y\right)\right)\right]$$

(6)

We have $V\left(L_1\ge L_2\right)=1$ if the pair $\left(x,y\right)$ exists with $x\ge y$ and ${\mu }_{L_1}\left(x\right)={\mu }_{L_2}\left(y\right)$.

Due to the fact that $L_1$ and $L_2$ are convex fuzzy numbers, we have:

$$V\left(L_1\ge L_2\right)=1, if l_1\ge l_2$$

(7)

and

$$\left(L_2\ge L_1\right)=hgt\left(L_1◠L_2\right)={\mu }_{L_1}\left(d\right)$$

(8)

The ordinate of the highest intersection point D between ${\mu }_{L_1}$ and ${\mu }_{L_2}$ is denoted by $d$.

The ordinate of point D is derived using $L_1=(o_1,p_1$, $q_1)$ and $L_2=(o_2,p_2$, $q_2)$ by (9):

$$V\left(L_2\ge L_1\right)=hgt\left(L_1◠L_2\right)=\frac{l_1-q_2}{\left(p_2-q_2\right)-\left(p_1-o_1\right)}$$

(9)

Calculate the values of $V\left(L_1\ge L_2\right)$ and $V\left(L_2\ge L_1\right)$ in order to compare $L_1$ and $L_2$.

$L_i\left(i=1,2,\dots k\right)$ is the probability of a convex fuzzy number being bigger than $k$ convex fuzzy numbers.

$$\left(L\ge L_1,L_2,\dots ,L_k\right)=V\left[\left(L\ge L_1\right) and \left(L\ge L_2\right)\right]$$

(10)

and, $(L\ge L_k$) = min V (L $\ge L_i),i=1,2,\dots ,k$

Under the premise that:

$$d^{\prime }\left(B_i\right)=minV\left(S_i\ge S_k\right)$$

(11)

for $k=1,2,\dots n \mathrm{and} k\#i$, the weight vector is calculated as follows:

$$W^{\prime }={\left(d^{\prime }\left(B_1\right),d^{\prime }\left(B_2\right),\dots d^{\prime }\left(B_n\right)\right)}^T$$

(12)

where $B_i$ is the number of elements, and $n$ is the number of elements.

The normalized weight vectors are represented as follows:

$$W={\left(d\left(B_1\right),d\left(B_2\right),\dots ,d\left(B_n\right)\right)}^T$$

(13)

The number $W$ is a nonfuzzy number.

The consistency of a Saaty’s matrix is determined by evaluating it.

$$CR=\frac{CI}{RI}=\frac{\overline{\lambda }-n}{\left(n-1\right)\times RI}\le 0.1$$

(14)

3.3. Interactive and Multi-Criteria Decision-Making Model from Portugal (TODIM)

The TODIM technique (Interactive and Multi-criteria Decision-Making in Portuguese) is a discrete multi-criteria method based on Prospect Theory that was developed in its current version at the beginning of the 1990s. The TODIM method’s primary steps are as follows [43]:

Step 1: Create a decision-making matrix.

Step 2: The total weights of all the criteria must equal to 1:

$$q_1+q_2+\dots +q_j=1; j=\overline{1,n}$$

(15)

Step 3: To achieve comparable values, quantitative criterion scales are standardized. To obtain comparable results, these estimations are normalized in the same way as quantitative scales are. The set of Equations (17)–(19) is used for maximizing criteria, while Equation (16) is used for minimizing criteria. Equation (17) is used to standardize values.

Equation (18) converts the larger values into smaller ones, giving the lower initial alternative estimations more weight. New values are normalized using Equation (19):

$${\overline{x}}_{ij}=\frac{{\overline{x}}_{ij}}{{{\displaystyle \sum }}_{i=1}^m{\overline{x}}_{ij}}; i=\overline{1,m}; j=\overline{1,n}$$

(16)

$${\overline{p}}_{ij}=\frac{{\overline{x}}_{ij}}{{{\displaystyle \sum }}_{i=1}^m{\overline{x}}_{ij}}; i=\overline{1,m}; j=\overline{1,n}$$

(17)

$${\overline{p}}_{ij}^{\prime }=\frac{\underset{j}{\min }{\overline{p}}_{ij}}{{\overline{p}}_{ij}}; i=\overline{1,m}; j=\overline{1,n}$$

(18)

$${\overline{x}}_{ij}=\frac{{\overline{p}}_{ij}^{\prime }}{{{\displaystyle \sum }}_{i=1}^m{\overline{p}}_{ij}^{\prime }}; i=\overline{1,m}; j=\overline{1,n}$$

(19)

Step 4: The most important criterion (criterion $c_j$ with the highest weight—$q_c$) is used to recalculate individual criterion weights.

$$q_{jc}=\frac{q_j}{q_c}; j=\overline{1,n}$$

(20)

Step 5: The “single-criterion dominance” is determined as follows for each criterion $j=\overline{1,n}$ and for two alternatives $a_i$ and $a_k$, $i,k=\overline{1,m}$:

$${\Phi }_i{a}_i,a_k=\{\begin{array}{c}-\sqrt{\frac{{{\displaystyle \sum }}_{j=1}^n{q}_{jc}\left|{\overline{x}}_{ij}-{\overline{x}}_{kj}\right|}{q_{jc}}, if {\overline{x}}_{ij}-{\overline{x}}_{kj}<0}\\ 0, if {\overline{x}}_{ij}-{\overline{x}}_{kj}=0\\ \sqrt{\frac{q_{jc}=\left|{\overline{x}}_{ij}-{\overline{x}}_{kj}\right|}{{{\displaystyle \sum }}_{j=1}^n{q}_{jc}}, if \left({\overline{x}}_{ij}-{\overline{x}}_{kj}\right)>0}\end{array}$$

(21)

i,k = $\overline{1,m}$, j = $\overline{1,n}$

Step 6: The “relative dominance” is determined as the sum of “single-criterion dominance” measurements for each pair of alternatives $a_i$ and $a_k$ i,k = $\overline{1,m}$:

$$\mathsf{\delta }(a_i, a_k)={{\displaystyle \sum }}_{j=1}^n{\Phi }_j(a_i,a_k);j=\overline{1,n}$$

(22)

Step 7: The “global overview” G($a_i$) of each option $a_i i$ = $\overline{1,m}$, m is calculated as a sum of “relative overview” over all other alternatives:

$$\mathrm{G}\left(a_i\right)={{\displaystyle \sum }}_{k=1}^m\mathsf{\delta }\left(a_i, a_k\right);k=\overline{1,m}$$

(23)

Step 8. The final stage uses the following equation to normalize “global dominances” to obtain the “relative overall value V($a_i$) of each alternative:

$$\mathrm{V}\left(a_i\right)=\frac{\mathrm{G}\left(a_i\right)-mi{n}_i\mathrm{G}\left(a_i\right)}{ma{x}_i\mathrm{G}\left(a_i\right)-mi{n}_i\mathrm{G}\left(a_i\right)} i=\overline{1,m}$$

(24)

The “relative overall values” ranging from 0 to 1 produced from Equation (24) are utilized to rank order alternatives.

4. Case Study

Vaccines are a great medical achievement of mankind. Every year, vaccines save nearly three million lives against dangerous diseases. Almost half of children worldwide are protected by vaccines from disease, disability, and death. In Vietnam, over the past 25 years, vaccines have protected more than 6.7 million children and prevented hundreds of thousands of deaths from deadly infectious diseases. Depending on the manufacturing method, there are several common types of vaccines: inactivated vaccines, live-attenuated vaccines, messenger RNA (mRNA) vaccines, subunit, recombinant, polysaccharide, and conjugate vaccines, toxoid vaccines, and viral vector vaccines. Should the requirements not be met, the quality of the vaccines, and in some serious cases, the health of the receivers, could be heavily affected. Hence, the selection process for a cold logistics supplier is crucial for manufacturers that require heavy preservation methods.

V is the first company to have the latest generation vaccines from the world’s leading manufacturers. All vaccines are imported genuine from major manufacturers in the world. R provides many flexible vaccination services according to customers’ requirements. With a system of many facilities stretching around Vietnam, V requires cold chain suppliers to meet GSP standards, a modern cold storage system, ensuring a storage temperature of 2–8 °C. Cold storage must be fully equipped with modern automatic temperature monitoring devices, a timely warning system when the temperature exceeds the allowable threshold, a variety of channels for receiving warning information, ensuring all vaccines are always stored in the best way. To ensure the quality of Vaccines, reduce the high cost during storage and transportation, and improve its competitiveness, V needs to select a suitable vaccines cold chain logistics service supplier.

In this study, the authors present an integrated MCDM method for evaluating and selecting cold chain logistics services providers with a case study in Vietnam. First, fuzzy AHP was applied to estimate the weights of all criteria. Then, the TODIM model was applied to rank the alternatives in final stage. List of criteria affecting the decision-making process is shown in

Table 1. List of criteria affecting the decision-making process.

No.	Criteria	Sub-Criteria	Literature Review	Experts	Symbol
1	Environmental factors	The green design of cold storages	Khan and Ali [44] Kannan et al. [45]	X	VC01
		CO2 emissions of refrigerated vehicle	Liao et al. [46]	X	VC02
		Utilization of refrigerant	Liao et al. [46]	X	VC03
2	Economic factors	IT applications for tracking and tracing	Singh et al. [47]	X	VC04
		Refrigeration infrastructure	Singh et al. [47]	X	VC05
		Cost of service	Singh et al. [47]	X	VC06
		Cold chain network management	Singh et al. [47] Agrawal et al. [48]	X	VC07
3	Social factors	Health and safety	Khan and Ali [44]	X	VC08
		Expertise and staff level	Ho et al. [49]	X	VC09
4	Service Level factors	Reliability and on-time delivery	Wen at al. [6]	X	VC10
		Product quality	Wen at al. [6] Govindan and Chaudhuri [50]	X	VC11
		Response speed and flexibility	Wen at al. [6] Govindan and Chaudhuri [50]	X	VC12

.

In the first stage, FAHP was applied to calculate the weight of the evaluation criteria for the assessment and selection of vaccine cold chain logistics service providers. There were four main criteria, including environmental factors, social factors, economic factors, and service level factors, which were separated into 12 subcriteria. There were ten experts who had been working in the area of cold chains for the past ten years invited to determine four potential vaccine cold chain logistics service providers (LC01, LC02, LC03, LC04) and 12 essential criteria, and input data of the FAHP model. Results of the FAHP model is shown in

Table 2. Results of the FAHP model.

Criteria	Fuzzy Sum of Each Row			Fuzzy Synthetic Extent			Degree of Possibility (Mi)	Normalization
VC01	9.6784	13.2990	18.3758	0.0438	0.0811	0.1544	0.6607	0.0777
VC02	9.0419	12.4555	16.9126	0.0409	0.0760	0.1421	0.6117	0.0719
VC03	12.9012	18.1699	24.1744	0.0584	0.1108	0.2031	0.9721	0.1143
VC04	9.3809	13.1380	18.0643	0.0424	0.0801	0.1518	0.6511	0.0766
VC05	13.6145	18.8357	24.8525	0.0616	0.1149	0.2088	1.0000	0.1176
VC06	7.8913	10.6839	14.6410	0.0357	0.0652	0.1230	0.5160	0.0607
VC07	8.5304	11.5994	15.6313	0.0386	0.0708	0.1313	0.5623	0.0661
VC08	10.4861	14.5276	19.1566	0.0474	0.0886	0.1609	0.7908	0.0930
VC09	10.5074	14.1979	18.5181	0.0475	0.0866	0.1556	0.7686	0.0904
VC10	8.3883	11.3433	15.6293	0.0379	0.0692	0.1313	0.6040	0.0710
VC11	7.4797	10.0780	13.9968	0.0338	0.0615	0.1176	0.5118	0.0602
VC12	11.1333	15.5972	21.1056	0.0504	0.0951	0.1773	0.8542	0.1005

.

In the next step, the TODIM ranked the potential alternatives. The preference weight of each criterion was obtained from the fuzzy AHP Model. According to the process of the TODIM approach, normalize matrix, sum of single criterion dominances [δ(ai,ak)] are shown in

Table 3. Normalize matrix of the TODIM model.

	LC01	LC02	LC03	LC04
VC01	0.22222	0.25926	0.29630	0.22222
VC02	0.25000	0.21875	0.25000	0.28125
VC03	0.25000	0.21875	0.25000	0.28125
VC04	0.26667	0.23333	0.20000	0.30000
VC05	0.25000	0.21875	0.25000	0.28125
VC06	0.24000	0.28000	0.20000	0.28000
VC07	0.25806	0.22581	0.29032	0.22581
VC08	0.23333	0.26667	0.30000	0.20000
VC09	0.28571	0.25000	0.21429	0.25000
VC10	0.24242	0.27273	0.21212	0.27273
VC11	0.26667	0.23333	0.30000	0.20000
VC12	0.27586	0.24138	0.20690	0.27586

and

Table 4. Sum of single criterion dominances [δ(ai,ak)].

	LC01	LC02	LC03	LC04
LC01	0	−2.32919	−2.93504	−3.60024
LC02	−4.80934	0	−4.72525	−3.74231
LC03	−3.8701	−3.54039	0	−6.05407
LC04	−2.66417	−1.91369	−3.75947	0

.

In this work, the authors introduced an integrated fuzzy MCDM model based on the combination of the Fuzzy Analytical Hierarchy Process (FAHP) model and an Interactive and Multi-criteria Decision-Making in Portuguese Model (TODIM) methods under the fuzzy linguistic environment. Using the fuzzy MCDM methodology is one of the strategies that can improve decision-making accuracy. This is a frequently used strategy that combines triangular fuzzy techniques to solve uncertainty from the decision-maker. In this work, the FAHP method derived criteria weights in the first stage, then, a TODIM method was presented to identify the ranking of logistics providers. To choose the best alternative by rank the values of V(ai), the alternative with maximum value was the best choice. As a result of the findings in

Table 5. Final ranking from TODIM model.

Alternatives	Global Dominance G(ai)	Relative Overall Value V(ai)	Rank
LC01	−8.8645	0.8972	2
LC02	−13.2769	0.0366	3
LC03	−13.4646	0.0000	4
LC04	−8.3373	1.0000	1

, LC04 had a closeness coefficient of 1.0, which was the maximum in this scenario; consequently, it was the best alternative for the company. This method was presented through a real-world case study that included nine evaluation criteria that the company used to establish the best green marketing strategy.

The purpose of the sensitivity analysis was to verify whether there were differences in the results of the selection of logistics service provider of vaccine cold chain under different θ values (representing the different ability of decision makers to avoid risks). In this paper, two values of θ = 3, 4 [51] were used for sensitivity analysis. The results for different values of θ variables in the TODIM method are given in

Table 6. Sensitivity analysis.

Alternatives	θ = 3	θ = 4	Rank
LC01	0.8234	0.8873	2
LC02	0.3320	0.0392	3
LC03	0.0000	0.0000	4
LC04	1.0000	1.0000	1

below. The fact that the sorting did not change in any case shows that the decision makers remained on the very safe side. This result was used to evaluate the proposed model’s robustness.

5. Conclusions

The selection and evaluation process for logistics suppliers in cold chains, especially those who deal with low-temperature storage, is considered from many factors to reduce the potential waste of products from poor storage strategies. Vaccine cold chain logistics service provider selection is a multiple-criteria decision-making (MCDM) problem. In this study, the authors proposed an MCDM model including a Fuzzy Analytical Hierarchy Process and the Interactive and Multi-criteria Decision-Making Model in Portuguese (TODIM) model methods under the fuzzy linguistic environment for logistics service provider selection in vaccine cold chains. First, the proposed approach was the first vaccine cold chain logistics provider evaluation and selection model in Vietnam using expert interviews and literature reviews. Second, this was the first study to provide a case study on evaluating logistics suppliers in vaccine cold chain logistics that utilized a combination of FAHP and TODIM models. The findings of this study may be used as a beneficial reference in analyzing and selecting the best vaccine cold chain logistics service provider, as well as for decision makers in other cold supply chains.